# Variable Definitions

**Reviewer Issue 3.1**: Clarify variable construction.

## Automation Proxies

| Label in Paper | Column Name | Source | Construction | Units |
|:---|:---|:---|:---|:---|
| Investment/GDP (I/Y) | capital_intensity | WDI | Gross capital formation / GDP | % of GDP |
| Capital-output ratio (K/Y) | capital_output_ratio | PWT 10.01 | rnna / rgdpo (constant 2017 prices) | Ratio |
| Capital per worker (K/L) | capital_per_worker | PWT 10.01 | rnna / (emp × 1M) | Millions per worker |
| GDP per capita | labor_productivity | WDI | GDP per capita, PPP (current intl $) | USD PPP |
| Labor share | labsh | PWT 10.01 | Share of labor compensation in GDP | 0–1 |
| Capital share | automation_proxy | PWT 10.01 | 1 − labsh | 0–1 |
| Trade openness | gvc_proxy | WDI | (Exports + Imports) / GDP | % of GDP |

## Coverage

| Variable | Non-missing obs | Countries | Years |
|:---|---:|---:|:---|
| capital_intensity | 6620 | 175 | 1980–2024 |
| capital_output_ratio | 10314 | 180 | 1950–2019 |
| capital_per_worker | 9479 | 180 | 1950–2019 |
| labor_productivity | 6553 | 189 | 1990–2024 |
| labsh | 7970 | 138 | 1950–2019 |
| gvc_proxy | 6797 | 177 | 1980–2024 |

## Key Distinction

**Investment/GDP (I/Y)** measures investment *effort* — the flow of new capital formation as a share of current output. It reflects how much of output is being directed toward capital accumulation in a given year.

**Capital-output ratio (K/Y)** measures the *stock* of capital relative to output. It reflects the accumulated capital intensity of the production structure. K/Y rises slowly as investment accumulates and depreciates.

**Capital per worker (K/L)** measures the capital available to each worker. It can diverge from K/Y when labor force growth differs from output growth (e.g., immigration raises L faster than K).

In earlier drafts, 'capital intensity' referred to I/Y. We now use explicit labels throughout to avoid ambiguity.